Suppose daily operating profit, in dollars, for a movie theater is a function of the number of tickets sold with the rule P (x) = 8.5x-2,500, for 0≤x≤1,000.

a) Explain why the profit function has an inverse b) P (400) = 900. Rewrite this equation in terms of P^-1.

c) Verify that P^-1 (4470) = 820 and describe what this equation means in this context.

d) Find a rule for P^-1 (x) and then verify the P^-1 (P (450)) = 450

Question

Armando Larson

Mathematics

25 January, 05:28

Suppose daily operating profit, in dollars, for a movie theater is a function of the number of tickets sold with the rule P (x) = 8.5x-2,500, for 0≤x≤1,000.

a) Explain why the profit function has an inverse b) P (400) = 900. Rewrite this equation in terms of P^-1.

c) Verify that P^-1 (4470) = 820 and describe what this equation means in this context.

d) Find a rule for P^-1 (x) and then verify the P^-1 (P (450)) = 450

+4

Answers (1)

Know the Answer?

Antwan Goodman · Answer 1

A. given a profit, there is only one number of tickets that could have been sold.

b. P^-1 (900) = 400

c. it means that 4470 of revenue translates to 820 tickets.

P (820) = 8.5 (820) - 2500=4470

D. i was not able to answer as i dont understand the question